Algebraic Geometry Seminar

The derived category of a cubic fourfold admits a decomposition with one
factor being strikingly similar to the derived category of a K3 surface.
For three special classes, one can construct geometrically a K3 which
derived embeds into the derived category of the fourfold. Using ideas from
the theory of homological projective duality one can then apply this idea
in a family, obtaining a new derived equivalence between Calabi-Yau
threefolds. This is joint work with Richard Thomas from Imperial College.